Sharon has just retired, and has $1000000$ dollars in her retirement account. The account will earn interest at an annual rate of $10$ percent, compounded monthly. At the end of each month, Sharon will withdraw a fixed amount to cover her living expenses.

Sharon wants her savings to last exactly $30$ years. How much money can she withdraw each month?

$($Give your answer in dollars, correct to the nearest cent.$)$

monthly withdrawal: $|$

What is the maximum amount that Sharon can withdraw each month if she wants her savings to last indefinitely?

monthly withdrawal: